A journey down the rabbit hole of Rubik's-style puzzles

A friend and I have a unspoken tradition of buying gag gifts for each other off our Amazon wish-lists, which amounts to us placing a bunch of random stuff on the lists to see what the other orders. Traditionally, it’s been music or movies, but we’ve definitely had some weird things come up — digital home thermostats, drill bits, and the like. Long ago, I placed a stickerless Dayan Megaminx (a dodecahedron shaped puzzle) on my list and forgot about it. I had no real interest in it, had no expectation of ever being able to solve it (I was a 2-minute 3×3 solver at the time), and, more than anything, thought it would be a funny item for the wishlist. Lo and behold, it arrived at my house last December. I messed with a few times, got frustrated, and stashed it on my shelf.

A couple days ago, my 19-month-old brought it over to me, having scrambled it on his way. My OCD thusly challenged, solve it I had to. Which meant learning how to solve it.

I approached it entirely intuitively after realizing through a couple web searches that it’s essentially a complicated 3×3 — with 12 faces (rather than six), each with 5 edges and 5 corners (rather than 4). I experimented a couple times and then, on my third, decided to give it a go on video. Here is the result — a 10-minute solve (excluding the last layer), presented at 3x speed:

(music: Overdub’s “Five Step,” a mashup of Dave Brubeck’s Take Five and Radiohead’s “15 Step” — two incredible songs on their own right, and both in the 5/4 meter)

Not the most elegant or impressive of solves, but not bad for a purely intuitive third attempt, either. I definitely learned a bunch through the solve, and would expect to speed up substantially with practice:

Starting with the bottom face cross (star) edges and following that with basic F2L was easy and definitely the right way to start. That completed the bottom two layers.

Doing adjacent second and third faces (both angled down) was a bit of a guess, but I think that made sense, too, and worked out well.

In the bottom half of the puzzle, that left two partially solved bottom-angled faces to solve, each with three corners and two edges shared with the top-angled faces — in a long v-shape.

Of those 5 pieces, I realized that the two higher corners could be solved at the end by thinking of them as resting at the bottom of an F2L slot conencted to the top face (as in a 3×3) — the slots highlighted in FIG 1 below.

What took me a while to figure out was how to solve the V-shaped two edges and corner between those — the highlighted pieces in FIG 2 — without disturbing the already-solved adjacent faces. With some experimenting, I realized that I could solve those by using the top layer, which could be turned without affecting anything already solved.

I did that by moving an edge and corner into the top layer; I paired them using F2L algorithms; then I connected those two pieces to the second edge while inserting the v-shaped trio of pieces into its ultimate slot. In the video, I wasted a lot of moves by first placing one of the edges into its correct spot and then using the top layer to pair the other two pieces. Ultimately, I had to move that earlier placed edge out of its slot in order to mate it to the corner/other-edge pair, so that first placement was a total waste.

(By the way, I have no idea if this is a common or efficient way of solving the Megaminx. If it turns out to be useful, I’ll do a quick tutorial video on it, since I couldn’t find any good videos addressing this particular aspect.)

A final point I realized only after the solve: Unlike F2L on a 3×3, most of the pairing on a Megaminx occurs when there is a lot of open unsolved space. I did a lot of unnecessary hiding/unhiding instinctively based on 3×3 F2L. Almost none of that was required. In fact, a lot of the pairing can be done on faces not a part of the F2L slot; just create the pair wherever convenient and then move the pair around the puzzle for insertion.

I stopped the clock when I reached the last layer, realizing that I don’t know Megaminx last layer algorithms for OLL or PLL. I hazarded a guess that the three-star tips forming an L was not unlike the L-shape during edge orientation on a 3×3, applying F U R U’ R’ F’. Surprisingly, that worked, flipping the other two star tips. At that point, though, I really had no idea how to orient the corners and then permute all of the pieces. I know all 21 3×3 PLLs, but don’t know how to map them onto a 5-edge, 5-corner face. A little bit of googling revealed what I should have guessed: Andy Klise has a great downloadable Megaminx guide. I’ll spend some time with that soon.

A fun puzzle that is more approachable than I would have guessed. Lots to learn about it still....